Question

Solve the following system of equations by the elimination method:

2x – 3y = 24, x – y = 13

Answer 1

Given the system of equations:

2x – 3y = 24, x – y = 13

Step 1: Multiply the second equation by 3 to align the coefficients of (y):

3(x – y) = 3(13)

⇒ 3x – 3y = 39

Now, the system becomes:

2x – 3⁢y = 24

3x – 3y = 39

Step 2: Subtract the first equation from the second to eliminate (y):

(3x – 3y) – (2x – 3y) = 39 – 24

3x – 3y – 2x + 3y = 15

x = 15

Step 3: Substitute (x = 15) into the second original equation (x – y = 13):

15 – y = 13 

⇒ y = 15 – 13

⇒ y = 2